As you know, the mobile first index is getting ready to expand in the upcoming weeks and some webmasters that still have desktop only sites are a bit nervous. If you still haven't read the official Google tips or the what you need to know you might not understand that desktop sites will be fine.
Google will crawl the desktop site from the view of a mobile phone browser, but it will be fine. It won't get that mobile-friendly ranking boost but that is an old boost that launched ages ago that it doesn't get now. But otherwise, it should be fine.
Of course, your mobile users won't be happy looking at your site on a screen that isn't optimized for it. But that is known and you are aware of that.
John Mueller posted on Twitter:
Regardless, for mobile first indexing, we use the site as it's visible on smartphones. If it's "desktop-friendly," it's usually still a site that could be viewed w/zooming & panning (ancient FrontPage sites often work fine with MFI, for example).
— John ☆.o(≧▽≦)o.☆ (@JohnMu) February 26, 2018
So what does Google see when they are completely mobile-first indexing and you are desktop? Well, I remember that Matt McGee runs a U2 fan site and he has not made his site mobile friendly yet - it is atu2.com. This is what Google might see:
See, you got to pinch and zoom to see stuff but Google will render the desktop version on the mobile crawler.
Of course, you should make your site mobile friendly but will the sky fall if you don't? Nope. Will your users be super happy if you made your site mobile-friendly? Yup.
Forum discussion at Twitter.